ODE No. 628

\[ y'(x)=\frac {1}{3} x \left (3 \sqrt {x^2+3 y(x)}-2\right ) \]

✓ Mathematica : cpu = 0.133185 (sec), leaf count = 33

DSolve[Derivative[1][y][x] == (x*(-2 + 3*Sqrt[x^2 + 3*y[x]]))/3,y[x],x]

\[\left \{\left \{y(x)\to \frac {1}{48} \left (9 x^4-16 x^2-54 c_1 x^2+81 c_1{}^2\right )\right \}\right \}\]

✓ Maple : cpu = 0.271 (sec), leaf count = 23

dsolve(diff(y(x),x) = 1/3*x*(-2+3*(x^2+3*y(x))^(1/2)),y(x))

\[c_{1} +\frac {x^{2}}{3}+\frac {4}{27}-\frac {4 \sqrt {x^{2}+3 y \left (x \right )}}{9} = 0\]